x=x^2+4x+5

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Solution for x=x^2+4x+5 equation: 


Simplifying
x = x2 + 4x + 5

Reorder the terms:
x = 5 + 4x + x2

Solving
x = 5 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
-5 + x + -4x + -1x2 = 5 + 4x + x2 + -5 + -4x + -1x2

Combine like terms: x + -4x = -3x
-5 + -3x + -1x2 = 5 + 4x + x2 + -5 + -4x + -1x2

Reorder the terms:
-5 + -3x + -1x2 = 5 + -5 + 4x + -4x + x2 + -1x2

Combine like terms: 5 + -5 = 0
-5 + -3x + -1x2 = 0 + 4x + -4x + x2 + -1x2
-5 + -3x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
-5 + -3x + -1x2 = 0 + x2 + -1x2
-5 + -3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5 + -3x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 3x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
5 + 3x + x2 = 0

Solving
5 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 3x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 3x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x + x2 = 0 + -5
3x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
3x + x2 = -5

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -5 + 2.25

Combine like terms: -5 + 2.25 = -2.75
2.25 + 3x + x2 = -2.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -2.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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